There should be a narcissist’s prayer for people who bury their heads in the sand.

That didn’t happen

And if it did, it’s contained online

And if it isn’t, it’s not popular

And if it is, you can ignore it

And if you can’t, ¯\(ツ)/¯

They’re the same picture.

The is me with my PhD thesis. I wrote it, submitted it, planned for an absolute grilling in the Viva, got waved through the Viva with just minor corrections for grammar, went overzealous with corrections, submitted for review, got accepted, finally graduated.

It still makes me sick to look at it on my bookshelf.

This really makes me grin, as I’ve argued these “theological debates” on multiple sides depending on which splatbook I’m into at the time. I’ve definitely been on both sides of the Caine vs Prime Archmage debate.

Jarl Balgruuf energy.

Do they have a different tattoo or are you referring to the one circling their arm? It looks like the inscription on the One Ring to me, though I definitely could be wrong.

You know you’re never going to get any hard evidence other than surface-level stuff that they can get from their bigot blogs, because bigots hate actually engaging with media.

Yes, there are infinities of larger magnitude. It’s not a simple intuitive comparison though. One might think “well there are twice as many whole numbers as even whole numbers, so the set of whole numbers is larger.” In fact they are the same size.

Two most commonly used in mathematics are countably infinite and uncountably infinite. A set is countably infinite if we can establish a one to one correspondence between the set of natural numbers (counting numbers) and that set. Examples are all whole numbers (divide by 2 if the natural number is even, add 1, divide by 2, and multiply by -1 if it’s odd) and rational numbers (this is more involved, basically you can get 2 copies of the natural numbers, associate each pair (a,b) to a rational number a/b then draw a snaking line through all the numbers to establish a correspondence with the natural numbers).

Uncountably infinite sets are just that, uncountable. It’s impossible to devise a logical and consistent way of saying “this is the first number in the set, this is the second,…) and somehow counting every single number in the set. The main example that someone would know is the real numbers, which contain all rational numbers and all irrational numbers including numbers such as e, π, Φ etc. which are not rational numbers but can either be described as solutions to rational algebraic equations (“what are the solutions to “x^2 - 2 = 0”) or as the limits of rational sequences.

Interestingly, the rational numbers are a dense subset within the real numbers. There’s some mathsy mumbo jumbo behind this statement, but a simplistic (and insufficient) argument is: pick 2 real numbers, then there exists a rational number between those two numbers. Still, despite the fact that the rationals are infinite, and dense within the reals, if it was possible to somehow place all the real numbers on a huge dartboard where every molecule of the dartboard is a number, then throwing a dart there is a 0% chance to hit a rational number and a 100% chance to hit an irrational number. This relies on more sophisticated maths techniques for measuring sets, but essentially the rationals are like a layer of inconsequential dust covering the real line.

There’s no problem at all with not understanding something, and I’d go so far as to say it’s virtuous to seek understanding. I’m talking about a certain phenomenon that is overrepresented in STEM discussions, of untrained people (who’ve probably took some internet IQ test) thinking they can hash out the subject as a function of raw brainpower. The ceiling for “natural talent” alone is actually incredibly low in any technical subject.

There’s nothing wrong with meming on a subject you’re not familiar with, in fact it’s often really funny. It’s the armchair experts in the thread trying to “umm actually…” the memer when their “experience” is a YouTube video at best.

I like this comment. It reads like a mathematician making a fun troll based on comparing rates of convergence (well, divergence considering the sets are unbounded). If you’re not a mathematician, it’s actually a really insightful comment.

So the value of the two sets isn’t some inherent characteristic of the two sets. It is a function which we apply to the sets. Both sets are a collection of bills. To the set of singles we assign one value function: “let the value of this set be $1 times the number of bills in this set.” To the set of hundreds we assign a second value function: “let the value of this set be $100 times the number of bills in this set.”

Now, if we compare the value restricted to two finite subsets (set within a set) of the same size, the subset of hundreds is valued at 100 times the subset of singles.

Comparing the infinite set of bills with the infinite set of 100s, there is no such difference in values. Since the two sets have unbounded size (i.e. if we pick any number N no matter how large, the size of these sets is larger) then naturally, any positive value function applied to these sets yields an unbounded number, no mater how large the value function is on the hundreds “I decide by fiat that a hundred dollar bill is worth $1million” and how small the value function is on the singles “I decide by fiat that a single is worth one millionth of a cent.”

In overly simplified (and only slightly wrong) terms, it’s because the sizes of the sets are so incalculably large compared to any positive value function, that these numbers just get absorbed by the larger number without perceivably changing anything.

The weight question is actually really good. You’ve essentially stumbled upon a comparison tool which is comparing the rates of convergence. As I said previously, comparing the value of two finite subsets of bills of the same size, we see that the value of the subset of hundreds is 100 times that of the subset of singles. This is a repeatable phenomenon no matter what size of finite set we choose. By making a long list of set sizes and values “one single is worth $1, 2 singles are worth $2,…” we can define a series which we can actually use for comparison reasons. Note that the next term in the series of hundreds always increases at a rate of 100 times that of the series of singles. Using analysis techniques, we conclude that the set of hundreds is approaching its (unbounded) limit at 100 times the rate of the singles.

The reason we cannot make such comparisons for the unbounded sets is that they’re unbounded. What is the weight of an unbounded number of hundreds? What is the weight of an unbounded number of collections of 100x singles?

This kind of thread is why I duck out of casual maths discussions as a maths PhD.

The two sets have the same value, that is the value of both sets is unbounded. The set of 100s approaches that value 100 times quicker than the set of singles. Completely intuitive to someone who’s taken first year undergraduate logic and calculus courses. Completely unintuitive to the lay person, and 100 lay people can come up with 100 different wrong conclusions based on incorrect rationalisations of the statement.

I’ve made an effort to just not participate since back when people were arguing Rick and Morty infinite universe bollocks. “Infinite universes means there are an infinite number of identical universes” really boils my blood.

It’s why I just say “algebra” when asked what I do. Even explaining my research (representation theory) to a tangentially related person, like a mathematical physicist, just ends in tedious non-discussion based on an incorrect framing of my work through their lens of understanding.

I’ve been experimenting with short rests. A 1-2 hour nap when I get home gives me the energy for activities, rather than droning through activities like a zombie for the sake of another couple hours.

Inventory management can be fun if implemented well by the system. See Traveller. “We’ve got 3dT of cargo space left. The locals are paying crap for petrochemicals but they’re having a fire sale on marble. If we basically give away that benzene that no one’s bought in 3 months, we can fill up on marble that some architect will definitely snatch up at the next class A starport.”

It’s a difficult one to rule, as suddenly being meticulous about positioning and line of sight telegraphs that the players should suddenly be focused on these things. I usually just have them roll luck or try to perceive the threat before they accidentally trigger its ability. If they fail, they get a Medusa blast

Please give it a spin if you haven’t already. Game mechanics need not be constrained to die roll plus modifier. Probably my favourite mechanic is that your level of aptitude in a skill is repesented by the size of die you roll. Also, Savage worlds were doing rerolls for good roleplay in the form of bennies for a few years before D&D dreamed up advantage and inspiration.

I also love playing a Huckster in Deadlands. The poker hand mechanic to essentially perform wild magic is ridiculously evocative.

I’m really singing its praises here, but I really love the classless edge system of Savage Worlds. I’ve never come up against the problem I have with other RPGs where I have to force the mechanics to fit my concept. Want a plate armoured wizard? 2 edges, playable as a beginner character.

I have started doing that actually. I’ve moved over mainly to Call of Cthulhu, which has very fast and easy combat. I’ve had some great descriptions of combat manoeuvres that net a bonus die.

Someone after my own heart. Say what you’re going to say and I’ll decide the DC. Just say “please” and probably get a straight check DC 12-14. Insult the guard’s mother and children will likely get a DC of at least 15 and maybe disadvantage. Going above and beyond probably doesn’t require a roll and nets you inspiration.

Savage Worlds does this right with wounds. Anything under a great success leaves the character shaken, so that they must save of lose their turn. Every wound is a cumulative -1 on all rolls. 4 wounds and you’re out of the fight.